The Universal Computer

Turing’s Analysis of the Computation Process

She has now shifted her attention to the digits 3 and 7 which are to be

multiplied in turn. After the phase of the computation in which she mul-

tiplies pairs of digits is completed, she will need to add her two “partial

products:”

⇓⇓

4 2 3 1 × 7 7 = 2 9 6 1 7 + 2 9 6 1 7 0 =

She begins this phase by adding the digits 7 and 0, obtaining:

⇓⇓

4 2 3 1 × 7 7 = 2 9 6 1 7 + 2 9 6 1 7 0 = 7

Now she must add the digits 1 and 7 to get 8. Notice that the digits that

have her attention at this point, 1 and 7, are the same digits that she

multiplied when she began the calculation. But although the digits are the

same, her ...